Sen. Rand Paul (R., Ky.) said he would vote against the nomination of Marvin Goodfriend for a spot on the Federal Reserve's board of governors, raising the prospect the Carnegie Mellon University economist might not have enough support to win confirmation.

Mr. Goodfriend hasn't attracted any Democratic support yet. If no Democrat or independent votes to confirm him, the GOP can lose no more than one of its votes in the Senate. Republicans have a 51-49 majority in the chamber.

The GOP's thin majority has been even more delicate due to the medical absence of Sen. John McCain (R., Ariz.), who is being treated for brain cancer. Last year, Vice President Mike Pence broke a 50-50 tie to secure confirmation for a handful of nominations where Republicans joined Democrats in opposition, but he wouldn't be able do that if all 47 Democrats and two independents oppose Mr. Goodfriend's nomination and Mr. McCain isn't present.